Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #23763444 | C2 | semidirect |
| 4. #23761521 | C2 | semidirect |
| 5. C79×#1391 | C2 | semidirect |
| 6. C2×#14579169 | C4 | semidirect |
| 12. #19098586 | C4 | semidirect |
| 14. #19098529 | C4 | semidirect |
| 15. C2×C8×Dic79 | C4 | semidirect |
| 155. #1391 | D79 | semidirect |
| 156. C79 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772108 | 2 |
| #23765063 | 2 |
| #23763444 | 2 |
| #23761521 | 2 |
| C79×#1391 | 2 |
| #12807 | 79 |